# Questions tagged [levy-processes]

Question related to Lévy processes, i.e. stochastically continuous processes with independent, stationary increments.

215 questions
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### Proving properties for the Poisson-process.

Define a Poisson process as a Levy process where the increments have a Poisson distribution with parameter $\lambda$*"length of increment". I want to prove these properties: It has almost surely ...
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### A proof by René Schilling that a continuous Lévy process is integrable

In his treatise "An Introduction to Lévy and Feller Processes" (arXiv link), Prof. Dr. René Schilling gives a short and seemingly straightforward proof for the claim that a continuous Lévy process is ...
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### Proof of strong Markov Property of double sided Levy Process

Let $(X_t)_{t\in\mathbb{R}}$ be a Levy Process, i.e. $X_0 = 0$ a.s., $X$ has independent and stationary increments, and almost all paths $t\mapsto X_t(\omega)$ are right continuous with left hand ...
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### Central Limit Theorem for a Lévy Process (mild assumptions)

I want to discuss the Central Limit Theorem (CLT) of a Lévy process under some assumptions. The answer of the previous post Central Limit Theorem for Lévy Process required a wide base of knowledge, ...
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### What is the Lévy measure of the Student's $t$-distribution?

It is known since the 1970's that the Student's $t$-distribution is infinitely divisible. We can therefore apply the Lévy-Khintchine representation to it, and define the Lévy measure associated to a ...
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### Bounded L2 increments for an Ornstein Uhlenbeck type process

Let $Z$ be an increasing Levy process (i.e. a subordinator). Let $\lambda>0$ and consider the Ornstein Uhlenbeck type SDE $$d V_t = - \lambda V_t dt + d Z_{\lambda t }$$ where the integral can e....